Is transparency kept?

Yes. AVIF stores an alpha channel and PNG does too, so a transparent background survives the conversion.

Why is the PNG bigger than the AVIF?

AVIF compresses much harder. PNG trades file size for exactness, which is the point of choosing it.

Not from a PNG here — this converter reads AVIF and WEBP. Converting a PNG to AVIF would need an AVIF encoder in the browser, which none has yet.

AVIF to PNG — lossless, transparency intact.